Estimating transform values using signal estimates

ABSTRACT

According to embodiments, estimated values for a signal transform may be generated using estimated values for the signal. Signal parameters may then be determined based on the estimated signal transform. A first portion of a signal may be obtained. A second portion of the signal may be estimated. The second portion of the signal may correspond to a portion of the that is unknown, that is not yet available and/or that is obscured by noise and/or artifacts. A transform (e.g., a continuous wavelet transform) of both of the signal portions may be performed. One or more parameters corresponding to the signal may then be determined from transformed signal.

SUMMARY

The present disclosure is related to signal processing systems andmethods, and more particularly, to systems and methods for estimatingvalues in a signal transform using estimated values for the signal.Parameters related to the signal may be determined based on theestimated signal transform.

In an embodiment, a signal transform (e.g., a continuous wavelettransform) may contain one or more regions in which the values of thetransform may be unknown or erroneous. These unknown or erroneoustransform values may be replaced with estimated transform values. Theestimated transform values may be generated by estimating values for thesignal used to compute the transform. The estimated signal values mayreplace portions of the signal that are unknown, that are not yetavailable (i.e., future signal values) and/or that are obscured by noiseand/or artifacts.

In an embodiment, a signal transform may contain a significant amount oferroneous transform values in a region around an end point of thesignal. This region may be referred to as an “edge effect” region. Whenthe transform is computed within the edge effect region, the end pointof the signal may appear within the computation as a sharp discontinuityin the signal. This apparent sharp discontinuity in the signal mayadversely affect the computed values of the transform in this region. Inorder to reduce the erroneous transform values in this edge effectregion, signal values may be estimated for the, as yet unknown, portionof the signal beyond the end point. The estimated signal values may thenbe used to compute the transform of the signal. In an embodiment, theestimated signal values may be set to a constant value such as, forexample, a current signal value or a mean signal value. In anembodiment, the estimated signal values may be an extrapolated estimateor fitted curve (i.e., a functional estimate) of the signal. In anembodiment, known signal types (e.g., a PPG signal) may be estimatedbased on characteristic values of the signal and/or information aboutthe origin of the signal.

In an embodiment, the transform may be a continuous wavelet transform. Acontinuous wavelet transform may be performed by computing a convolution(or any other suitable cross-correlation) of the signal with wavelets atvarious scales. Within an edge effect region (or any other similarregion) any computed transform values may be incomplete because thesignal values required to fully resolve the transform for a particulartime period may not be known or available. At higher scales the smallerwavelet scale sizes may result in a smaller edge effect region. At lowerscales the larger wavelet scale sizes may result in a larger edge effectregion. The size of the estimated signal portions may therefore dependon the scales at which the transform is computed.

In an embodiment, the transformed signal may be a photoplethysmograph(PPG) signal. A first portion of the PPG signal may be obtained. Thefirst portion of the PPG signal may have an end point because additionalsignal values have not yet arrived. A second portion of the PPG signalmay be estimated. The second portion of the PPG signal may correspond toa portion of the signal beyond the end point of the first signalportion. A transform (e.g., a continuous wavelet transform) of thesignal portions may be performed. One or more biological parameters maybe determined based on the transformed signal including, for example,blood oxygen saturation level, respiration rate, respiration effortmetric, pulse rate, and/or blood pressure.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present disclosure, its nature andvarious advantages will be more apparent upon consideration of thefollowing detailed description, taken in conjunction with theaccompanying drawings in which:

FIG. 1 shows an illustrative pulse oximetry system in accordance with anembodiment;

FIG. 2 is a block diagram of the illustrative pulse oximetry system ofFIG. 1 coupled to a patient in accordance with an embodiment;

FIGS. 3( a) and 3(b) show illustrative views of a scalogram derived froma PPG signal in accordance with an embodiment;

FIG. 3( c) shows an illustrative scalogram derived from a signalcontaining two pertinent components in accordance with an embodiment;

FIG. 3( d) shows an illustrative schematic of signals associated with aridge in FIG. 3( c) and illustrative schematics of a further waveletdecomposition of these newly derived signals in accordance with anembodiment;

FIGS. 3( e) and 3(f) are flow charts of illustrative steps involved inperforming an inverse continuous wavelet transform in accordance withembodiments;

FIG. 4 is a block diagram of an illustrative continuous waveletprocessing system in accordance with some embodiments;

FIG. 5 is an illustrative plot of a scalogram in accordance with someembodiments;

FIG. 6 is an illustrative plot of a signal and a scalogram generatedfrom that signal that schematically illustrates a process for estimatingvalues for a transform using a signal estimate in accordance with someembodiments;

FIG. 7 depicts an illustrative process for determining parameters of asignal using estimated transform values generated from signal estimatesin accordance with some embodiments;

FIG. 8 depicts an illustrative process for estimating the values of aportion of a signal in accordance with some embodiments; and

FIG. 9 depicts an illustrative process for performing a transform of asignal using estimated portions of the signal in accordance with someembodiments.

DETAILED DESCRIPTION

An oximeter is a medical device that may determine the oxygen saturationof the blood. One common type of oximeter is a pulse oximeter, which mayindirectly measure the oxygen saturation of a patient's blood (asopposed to measuring oxygen saturation directly by analyzing a bloodsample taken from the patient) and changes in blood volume in the skin.Ancillary to the blood oxygen saturation measurement, pulse oximetersmay also be used to measure the pulse rate of the patient. Pulseoximeters typically measure and display various blood flowcharacteristics including, but not limited to, the oxygen saturation ofhemoglobin in arterial blood.

An oximeter may include a light sensor that is placed at a site on apatient, typically a fingertip, toe, forehead or earlobe, or in the caseof a neonate, across a foot. The oximeter may pass light using a lightsource through blood perfused tissue and photoelectrically sense theabsorption of light in the tissue. For example, the oximeter may measurethe intensity of light that is received at the light sensor as afunction of time. A signal representing light intensity versus time or amathematical manipulation of this signal (e.g., a scaled versionthereof, a log taken thereof a scaled version of a log taken thereofetc.) may be referred to as the photoplethysmograph (PPG) signal. Inaddition, the term “PPG signal” as used herein, may also refer to anabsorption signal (i.e., representing the amount of light absorbed bythe tissue) or any suitable mathematical manipulation thereof. The lightintensity or the amount of light absorbed may then be used to calculatethe amount of the blood constituent (e.g., oxyhemoglobin) being measuredas well as the pulse rate and when each individual pulse occurs.

The light passed through the tissue is selected to be of one or morewavelengths that are absorbed by the blood in an amount representativeof the amount of the blood constituent present in the blood. The amountof light passed through the tissue varies in accordance with thechanging amount of blood constituent in the tissue and the related lightabsorption. Red and infrared wavelengths may be used because it has beenobserved that highly oxygenated blood will absorb relatively less redlight and more infrared light than blood with a lower oxygen saturation.By comparing the intensities of two wavelengths at different points inthe pulse cycle, it is possible to estimate the blood oxygen saturationof hemoglobin in arterial blood.

When the measured blood parameter is the oxygen saturation ofhemoglobin, a convenient starting point assumes a saturation calculationbased on Lambert-Beer's law. The following notation will be used herein:I(λ,t)=I _(o)(λ)exp(−(sβ _(o)(λ)+(1−s)β_(r)(λ))l(t))  (1)where:λ=wavelength;t=time;I=intensity of light detected;

-   I_(o)=intensity of light transmitted;    s=oxygen saturation;    β_(o), β_(r)=empirically derived absorption coefficients; and    l(t)=a combination of concentration and path length from emitter to    detector as a function of time.

The traditional approach measures light absorption at two wavelengths(e.g., red and infrared (IR)), and then calculates saturation by solvingfor the “ratio of ratios” as follows.

1. First, the natural logarithm of (1) is taken (“log” will be used torepresent the natural logarithm) for IR and Redlog I=log I _(o)−(sβ _(o)+(1−s)β_(r))l  (2)2. (2) is then differentiated with respect to time

$\begin{matrix}{\frac{{\mathbb{d}\log}\; I}{\mathbb{d}t} = {{- \left( {{s\;\beta_{o}} + {\left( {1 - s} \right)\beta_{r}}} \right)}\frac{\mathbb{d}l}{\mathbb{d}t}}} & (3)\end{matrix}$3. Red (3) is divided by IR (3)

$\begin{matrix}{\frac{{\mathbb{d}\log}\;{{I\left( \lambda_{R} \right)}/{\mathbb{d}t}}}{{\mathbb{d}\log}\;{{I\left( \lambda_{IR} \right)}/{\mathbb{d}t}}} = \frac{{s\;{\beta_{o}\left( \lambda_{R} \right)}} + {\left( {1 - s} \right){\beta_{r}\left( \lambda_{R} \right)}}}{{s\;{\beta_{o}\left( \lambda_{IR} \right)}} + {\left( {1 - s} \right){\beta_{r}\left( \lambda_{IR} \right)}}}} & (4)\end{matrix}$4. Solving for s

$s = \frac{{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{IR} \right)}}{\mathbb{d}t}{\beta_{r}\left( \lambda_{R} \right)}} - {\frac{{\mathbb{d}\log}\;{I\left( \lambda_{R} \right)}}{\mathbb{d}t}{\beta_{r}\left( \lambda_{IR} \right)}}}{{{{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{R} \right)}}{\mathbb{d}t}\left( {{\beta_{o}\left( \lambda_{IR} \right)} - {\beta_{r}\left( \lambda_{IR} \right)}} \right)} -}\quad}\frac{{\mathbb{d}\log}\;{I\left( \lambda_{IR} \right)}}{\mathbb{d}t}\left( {{\beta_{o}\left( \lambda_{R} \right)} - {\beta_{r}\left( \lambda_{R} \right)}} \right)}$Note in discrete time

$\frac{{\mathbb{d}\log}\;{I\left( {\lambda,t} \right)}}{\mathbb{d}t} \simeq {{\log\;{I\left( {\lambda,t_{2}} \right)}} - {\log\;{I\left( {\lambda,t_{1}} \right)}}}$Using log A−log B=log A/B,

$\frac{{\mathbb{d}\log}\;{I\left( {\lambda,t} \right)}}{\mathbb{d}t} \simeq {\log\left( \frac{I\left( {t_{2},\lambda} \right)}{I\left( {t_{1},\lambda} \right)} \right)}$So, (4) can be rewritten as

$\begin{matrix}{{\frac{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{R} \right)}}{\mathbb{d}t}}{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{IR} \right)}}{\mathbb{d}t}} \simeq \frac{\log\left( \frac{I\left( {t_{1},\lambda_{R}} \right)}{I\left( {t_{2},\lambda_{R}} \right)} \right)}{\log\left( \frac{I\left( {t_{1},\lambda_{IR}} \right)}{I\left( {t_{2},\lambda_{IR}} \right)} \right)}} = R} & (5)\end{matrix}$where R represents the “ratio of ratios.” Solving (4) for s using (5)gives

$s = {\frac{{\beta_{r}\left( \lambda_{R} \right)} - {R\;{\beta_{r}\left( \lambda_{IR} \right)}}}{{R\left( {{\beta_{o}\left( \lambda_{IR} \right)} - {\beta_{r}\left( \lambda_{IR} \right)}} \right)} - {\beta_{o}\left( \lambda_{R} \right)} + {\beta_{r}\left( \lambda_{R} \right)}}.}$From (5), R can be calculated using two points (e.g., PPG maximum andminimum), or a family of points. One method using a family of pointsuses a modified version of (5). Using the relationship

$\begin{matrix}{\frac{{\mathbb{d}\log}\; I}{\mathbb{d}t} = \frac{{\mathbb{d}I}/{\mathbb{d}t}}{I}} & (6)\end{matrix}$now (5) becomes

$\begin{matrix}\begin{matrix}{\frac{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{R} \right)}}{\mathbb{d}t}}{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{IR} \right)}}{\mathbb{d}t}} \simeq \frac{\frac{{I\left( {t_{2},\lambda_{R}} \right)} - {I\left( {t_{1},\lambda_{R}} \right)}}{I\left( {t_{1},\lambda_{R}} \right)}}{\frac{{I\left( {t_{2},\lambda_{IR}} \right)} - {I\left( {t_{1},\lambda_{IR}} \right)}}{I\left( {t_{1},\lambda_{IR}} \right)}}} \\{= \frac{\left\lbrack {{I\left( {t_{2},\lambda_{R}} \right)} - {I\left( {t_{1},\lambda_{R}} \right)}} \right\rbrack{I\left( {t_{1},\lambda_{IR}} \right)}}{\left\lbrack {{I\left( {t_{2},\lambda_{IR}} \right)} - {I\left( {t_{1},\lambda_{IR}} \right)}} \right\rbrack{I\left( {t_{1},\lambda_{R}} \right)}}} \\{= R}\end{matrix} & (7)\end{matrix}$which defines a cluster of points whose slope of y versus x will give Rwherex(t)=[I(t ₂,λ_(IR))−I(t ₁,λ_(IR))]I(t ₁,λ_(IR))y(t)=[I(t ₂,λ_(R))−I(t ₁,λ_(R))]I(t ₁,λ_(IR))y(t)=Rx(t)  (8)

FIG. 1 is a perspective view of an embodiment of a pulse oximetry system10. System 10 may include a sensor 12 and a pulse oximetry monitor 14.Sensor 12 may include an emitter 16 for emitting light at two or morewavelengths into a patient's tissue. A detector 18 may also be providedin sensor 12 for detecting the light originally from emitter 16 thatemanates from the patient's tissue after passing through the tissue.

According to another embodiment and as will be described, system 10 mayinclude a plurality of sensors forming a sensor array in lieu of singlesensor 12. Each of the sensors of the sensor array may be acomplementary metal oxide semiconductor (CMOS) sensor. Alternatively,each sensor of the array may be charged coupled device (CCD) sensor. Inanother embodiment, the sensor array may be made up of a combination ofCMOS and CCD sensors. The CCD sensor may comprise a photoactive regionand a transmission region for receiving and transmitting data whereasthe CMOS sensor may be made up of an integrated circuit having an arrayof pixel sensors. Each pixel may have a photodetector and an activeamplifier.

According to an embodiment, emitter 16 and detector 18 may be onopposite sides of a digit such as a finger or toe, in which case thelight that is emanating from the tissue has passed completely throughthe digit. In an embodiment, emitter 16 and detector 18 may be arrangedso that light from emitter 16 penetrates the tissue and is reflected bythe tissue into detector 18, such as a sensor designed to obtain pulseoximetry data from a patient's forehead.

In an embodiment, the sensor or sensor array may be connected to anddraw its power from monitor 14 as shown. In another embodiment, thesensor may be wirelessly connected to monitor 14 and include its ownbattery or similar power supply (not shown). Monitor 14 may beconfigured to calculate physiological parameters based at least in parton data received from sensor 12 relating to light emission anddetection. In an alternative embodiment, the calculations may beperformed on the monitoring device itself and the result of the oximetryreading may be passed to monitor 14. Further, monitor 14 may include adisplay 20 configured to display the physiological parameters or otherinformation about the system. In the embodiment shown, monitor 14 mayalso include a speaker 22 to provide an audible sound that may be usedin various other embodiments, such as for example, sounding an audiblealarm in the event that a patient's physiological parameters are notwithin a predefined normal range.

In an embodiment, sensor 12, or the sensor array, may be communicativelycoupled to monitor 14 via a cable 24. However, in other embodiments, awireless transmission device (not shown) or the like may be used insteadof or in addition to cable 24.

In the illustrated embodiment, pulse oximetry system 10 may also includea multi-parameter patient monitor 26. The monitor may be cathode raytube type, a flat panel display (as shown) such as a liquid crystaldisplay (LCD) or a plasma display, or any other type of monitor nowknown or later developed. Multi-parameter patient monitor 26 may beconfigured to calculate physiological parameters and to provide adisplay 28 for information from monitor 14 and from other medicalmonitoring devices or systems (not shown). For example, multiparameterpatient monitor 26 may be configured to display an estimate of apatient's blood oxygen saturation generated by pulse oximetry monitor 14(referred to as an “SpO₂” measurement), pulse rate information frommonitor 14 and blood pressure from a blood pressure monitor (not shown)on display 28.

Monitor 14 may be communicatively coupled to multi-parameter patientmonitor 26 via a cable 32 or 34 that is coupled to a sensor input portor a digital communications port, respectively and/or may communicatewirelessly (not shown). In addition, monitor 14 and/or multi-parameterpatient monitor 26 may be coupled to a network to enable the sharing ofinformation with servers or other workstations (not shown). Monitor 14may be powered by a battery (not shown) or by a conventional powersource such as a wall outlet.

FIG. 2 is a block diagram of a pulse oximetry system, such as pulseoximetry system 10 of FIG. 1, which may be coupled to a patient 40 inaccordance with an embodiment. Certain illustrative components of sensor12 and monitor 14 are illustrated in FIG. 2. Sensor 12 may includeemitter 16, detector 18, and encoder 42. In the embodiment shown,emitter 16 may be configured to emit at least two wavelengths of light(e.g., RED and IR) into a patients tissue 40. Hence, emitter 16 mayinclude a RED light emitting light source such as RED light emittingdiode (LED) 44 and an JR light emitting light source such as IR LED 46for emitting light into the patient's tissue 40 at the wavelengths usedto calculate the patient's physiological parameters. In one embodiment,the RED wavelength may be between about 600 nm and about 700 nm, and theIR wavelength may be between about 800 nm and about 1000 nm. Inembodiments where a sensor array is used in place of single sensor, eachsensor may be configured to emit a single wavelength. For example, afirst sensor emits only a RED light while a second only emits an IRlight.

It will be understood that, as used herein, the term “light” may referto energy produced by radiative sources and may include one or more ofultrasound, radio, microwave, millimeter wave, infrared, visible,ultraviolet, gamma ray or X-ray electromagnetic radiation. As usedherein, light may also include any wavelength within the radio,microwave, infrared, visible, ultraviolet, or X-ray spectra, and thatany suitable wavelength of electromagnetic radiation may be appropriatefor use with the present techniques. Detector 18 may be chosen to bespecifically sensitive to the chosen targeted energy spectrum of theemitter 16.

In an embodiment, detector 18 may be configured to detect the intensityof light at the RED and IR wavelengths. Alternatively, each sensor inthe array may be configured to detect an intensity of a singlewavelength. In operation, light may enter detector 18 after passingthrough the patient's tissue 40. Detector 18 may convert the intensityof the received light into an electrical signal. The light intensity isdirectly related to the absorbance and/or reflectance of light in thetissue 40. That is, when more light at a certain wavelength is absorbedor reflected, less light of that wavelength is received from the tissueby the detector 18. After converting the received light to an electricalsignal, detector 18 may send the signal to monitor 14, wherephysiological parameters may be calculated based on the absorption ofthe RED and IR wavelengths in the patients tissue 40.

In an embodiment, encoder 42 may contain information about sensor 12,such as what type of sensor it is (e.g., whether the sensor is intendedfor placement on a forehead or digit) and the wavelengths of lightemitted by emitter 16. This information may be used by monitor 14 toselect appropriate algorithms, lookup tables and/or calibrationcoefficients stored in monitor 14 for calculating the patient'sphysiological parameters.

Encoder 42 may contain information specific to patient 40, such as, forexample, the patient's age, weight, and diagnosis. This information mayallow monitor 14 to determine, for example, patient-specific thresholdranges in which the patient's physiological parameter measurementsshould fall and to enable or disable additional physiological parameteralgorithms. Encoder 42 may, for instance, be a coded resistor whichstores values corresponding to the type of sensor 12 or the type of eachsensor in the sensor array, the wavelengths of light emitted by emitter16 on each sensor of the sensor array, and/or the patient'scharacteristics. In another embodiment, encoder 42 may include a memoryon which one or more of the following information may be stored forcommunication to monitor 14: the type of the sensor 12; the wavelengthsof light emitted by emitter 16; the particular wavelength each sensor inthe sensor array is monitoring; a signal threshold for each sensor inthe sensor array; any other suitable information; or any combinationthereof.

In an embodiment, signals from detector 18 and encoder 42 may betransmitted to monitor 14. In the embodiment shown, monitor 14 mayinclude a general-purpose microprocessor 48 connected to an internal bus50. Microprocessor 48 may be adapted to execute software, which mayinclude an operating system and one or more applications, as part ofperforming the functions described herein. Also connected to bus 50 maybe a read-only memory (ROM) 52, a random access memory (RAM) 54, userinputs 56, display 20, and speaker 22.

RAM 54 and ROM 52 are illustrated by way of example, and not limitation.Any suitable computer-readable media may be used in the system for datastorage. Computer-readable media are capable of storing information thatcan be interpreted by microprocessor 48. This information may be data ormay take the form of computer-executable instructions, such as softwareapplications, that cause the microprocessor to perform certain functionsand/or computer-implemented methods. Depending on the embodiment, suchcomputer-readable media may include computer storage media andcommunication media. Computer storage media may include volatile andnon-volatile, removable and non-removable media implemented in anymethod or technology for storage of information such ascomputer-readable instructions, data structures, program modules orother data. Computer storage media may include, but is not limited to,RAM, ROM, EPROM, EEPROM, flash memory or other solid state memorytechnology, CD-ROM, DVD, or other optical storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other medium which can be used to store the desired informationand which can be accessed by components of the system.

In the embodiment shown, a time processing unit (TPU) 58 may providetiming control signals to a light drive circuitry 60, which may controlwhen emitter 16 is illuminated and multiplexed timing for the RED LED 44and the IR LED 46. TPU 58 may also control the gating-in of signals fromdetector 18 through an amplifier 62 and a switching circuit 64. Thesesignals are sampled at the proper time, depending upon which lightsource is illuminated. The received signal from detector 18 may bepassed through an amplifier 66, a low pass filter 68, and ananalog-to-digital converter 70. The digital data may then be stored in aqueued serial module (QSM) 72 (or buffer) for later downloading to RAM54 as QSM 72 fills up. In one embodiment, there may be multiple separateparallel paths having amplifier 66, filter 68, and A/D converter 70 formultiple light wavelengths or spectra received.

In an embodiment, microprocessor 48 may determine the patient'sphysiological parameters, such as SpO₂ and pulse rate, using variousalgorithms and/or look-up tables based on the value of the receivedsignals and/or data corresponding to the light received by detector 18.Signals corresponding to information about patient 40, and particularlyabout the intensity of light emanating from a patients tissue over time,may be transmitted from encoder 42 to a decoder 74. These signals mayinclude, for example, encoded information relating to patientcharacteristics. Decoder 74 may translate these signals to enable themicroprocessor to determine the thresholds based on algorithms orlook-up tables stored in ROM 52. User inputs 56 may be used to enterinformation about the patient, such as age, weight, height, diagnosis,medications, treatments, and so forth. In an embodiment, display 20 mayexhibit a list of values which may generally apply to the patient, suchas, for example, age ranges or medication families, which the user mayselect using user inputs 56.

The optical signal through the tissue can be degraded by noise, amongother sources. One source of noise is ambient light that reaches thelight detector. Another source of noise is electromagnetic coupling fromother electronic instruments. Movement of the patient also introducesnoise and affects the signal. For example, the contact between thedetector and the skin, or the emitter and the skin, can be temporarilydisrupted when movement causes either to move away from the skin. Inaddition, because blood is a fluid, it responds differently than thesurrounding tissue to inertial effects, thus resulting in momentarychanges in volume at the point to which the oximeter probe is attached.

Noise (e.g., from patient movement) can degrade a pulse oximetry signalrelied upon by a physician, without the physician's awareness. This isespecially true if the monitoring of the patient is remote, the motionis too small to be observed, or the doctor is watching the instrument orother parts of the patient, and not the sensor site. Processing pulseoximetry (i.e., PPG) signals may involve operations that reduce theamount of noise present in the signals or otherwise identify noisecomponents in order to prevent them from affecting measurements ofphysiological parameters derived from the PPG signals.

It will be understood that the present disclosure is applicable to anysuitable signals and that PPG signals are used merely for illustrativepurposes. Those skilled in the art will recognize that the presentdisclosure has wide applicability to other signals including, but notlimited to other biosignals (e.g. electrocardiogram,electroencephalogram, electrogastrogram, electromyogram, heart ratesignals, pathological sounds, ultrasound, or any other suitablebiosignal), dynamic signals, non-destructive testing signals, conditionmonitoring signals, fluid signals, geophysical signals, astronomicalsignals, electrical signals, financial signals including financialindices, sound and speech signals, chemical signals, meteorologicalsignals including climate signals, and/or any other suitable signal,and/or any combination thereof.

In one embodiment, a PPG signal may be transformed using a continuouswavelet transform. Information derived from the transform of the PPGsignal (i.e., in wavelet space) may be used to provide measurements ofone or more physiological parameters.

The continuous wavelet transform of a signal x(t) in accordance with thepresent disclosure may be defined as

$\begin{matrix}{{T\left( {a,b} \right)} = {\frac{1}{\sqrt{a}}{\int_{- \infty}^{+ \infty}{{x(t)}{\psi^{*}\left( \frac{t - b}{a} \right)}\ {\mathbb{d}t}}}}} & (9)\end{matrix}$where ψ*(t) is the complex conjugate of the wavelet function ψ(t), a isthe dilation parameter of the wavelet and b is the location parameter ofthe wavelet. The transform given by equation (9) may be used toconstruct a representation of a signal on a transform surface. Thetransform may be regarded as a time-scale representation. Wavelets arecomposed of a range of frequencies, one of which may be denoted as thecharacteristic frequency of the wavelet, where the characteristicfrequency associated with the wavelet is inversely proportional to thescale a. One example of a characteristic frequency is the dominantfrequency. Each scale of a particular wavelet may have a differentcharacteristic frequency. The underlying mathematical detail requiredfor the implementation within a time-scale can be found, for example, inPaul S. Addison, The Illustrated Wavelet Transform Handbook (Taylor &Francis Group 2002), which is hereby incorporated by reference herein inits entirety.

The continuous wavelet transform decomposes a signal using wavelets,which are generally highly localized in time. The continuous wavelettransform may provide a higher resolution relative to discretetransforms, thus providing the ability to garner more information fromsignals than typical fiequency transforms such as Fourier transforms (orany other spectral techniques) or discrete wavelet transforms.Continuous wavelet transforms allow for the use of a range of waveletswith scales spanning the scales of interest of a signal such that smallscale signal components correlate well with the smaller scale waveletsand thus manifest at high energies at smaller scales in the transform.Likewise, large scale signal components correlate well with the largerscale wavelets and thus manifest at high energies at larger scales inthe transform. Thus, components at different scales may be separated andextracted in the wavelet transform domain. Moreover, the use of acontinuous range of wavelets in scale and time position allows for ahigher resolution transform than is possible relative to discretetechniques.

In addition, transforms and operations that convert a signal or anyother type of data into a spectral (i.e., frequency) domain necessarilycreate a series of frequency transform values in a two-dimensionalcoordinate system where the two dimensions may be frequency and, forexample, amplitude. For example, any type of Fourier transform wouldgenerate such a two-dimensional spectrum. In contrast, wavelettransforms, such as continuous wavelet transforms, are required to bedefined in a three-dimensional coordinate system and generate a surfacewith dimensions of time, scale and, for example, amplitude. Hence,operations performed in a spectral domain cannot be performed in thewavelet domain; instead the wavelet surface must be transformed into aspectrum (i.e., by performing an inverse wavelet transform to convertthe wavelet surface into the time domain and then performing a spectraltransform from the time domain). Conversely, operations performed in thewavelet domain cannot be performed in the spectral domain; instead aspectrum must first be transformed into a wavelet surface (i.e., byperforming an inverse spectral transform to convert the spectral domaininto the time domain and then performing a wavelet transform from thetime domain). Nor does a cross-section of the three-dimensional waveletsurface along, for example, a particular point in time equate to afrequency spectrum upon which spectral-based techniques may be used. Atleast because wavelet space includes a time dimension, spectraltechniques and wavelet techniques are not interchangeable. It will beunderstood that converting a system that relies on spectral domainprocessing to one that relies on wavelet space processing would requiresignificant and fundamental modifications to the system in order toaccommodate the wavelet space processing (e.g., to derive arepresentative energy value for a signal or part of a signal requiresintegrating twice, across time and scale, in the wavelet domain while,conversely, one integration across frequency is required to derive arepresentative energy value from a spectral domain). As a furtherexample, to reconstruct a temporal signal requires integrating twice,across time and scale, in the wavelet domain while, conversely, oneintegration across frequency is required to derive a temporal signalfrom a spectral domain. It is well known in the art that, in addition toor as an alternative to amplitude, parameters such as energy density,modulus, phase, among others may all be generated using such transformsand that these parameters have distinctly different contexts andmeanings when defined in a two-dimensional frequency coordinate systemrather than a three-dimensional wavelet coordinate system. For example,the phase of a Fourier system is calculated with respect to a singleorigin for all frequencies while the phase for a wavelet system isunfolded into two dimensions with respect to a wavelet's location (oftenin time) and scale.

The energy density function of the wavelet transform, the scalogram, isdefined asS(a,b)=|T(a,b)|²  (10)where ‘∥’ is the modulus operator. The scalogram may be resealed foruseful purposes. One common rescaling is defined as

$\begin{matrix}{{S_{R}\left( {a,b} \right)} = \frac{{{T\left( {a,b} \right)}}^{2}}{a}} & (11)\end{matrix}$and is useful for defining ridges in wavelet space when, for example,the Morlet wavelet is used. Ridges are defined as the locus of points oflocal maxima in the plane. Any reasonable definition of a ridge may beemployed in the method. Also included as a definition of a ridge hereinare paths displaced from the locus of the local maxima. A ridgeassociated with only the locus of points of local maxima in the planeare labeled a “maxima ridge”.

For implementations requiring fast numerical computation, the wavelettransform may be expressed as an approximation using Fourier transforms.Pursuant to the convolution theorem, because the wavelet transform isthe cross-correlation of the signal with the wavelet function, thewavelet transform may be approximated in terms of an inverse FFT of theproduct of the Fourier transform of the signal and the Fourier transformof the wavelet for each required a scale and then multiplying the resultby √{square root over (a)}.

In the discussion of the technology which follows herein, the“scalogram” may be taken to include all suitable forms of resealingincluding, but not limited to, the original unsealed waveletrepresentation, linear resealing, any power of the modulus of thewavelet transform, or any other suitable resealing. In addition, forpurposes of clarity and conciseness, the term “scalogram” shall be takento mean the wavelet transform, T(a,b) itself, or any part thereof. Forexample, the real part of the wavelet transform, the imaginary part ofthe wavelet transform, the phase of the wavelet transform, any othersuitable part of the wavelet transform, or any combination thereof isintended to be conveyed by the term “scalogram”.

A scale, which may be interpreted as a representative temporal period,may be converted to a characteristic frequency of the wavelet function.The characteristic frequency associated with a wavelet of arbitrary ascale is given by

$\begin{matrix}{f = \frac{f_{c}}{a}} & (12)\end{matrix}$where f_(c), the characteristic frequency of the mother wavelet (i.e.,at a=1), becomes a scaling constant and f is the representative orcharacteristic frequency for the wavelet at arbitrary scale a.

Any suitable wavelet function may be used in connection with the presentdisclosure. One of the most commonly used complex wavelets, the Morletwavelet, is defined as:ψ(t)=π^(−1/4)(e ^(i2πf) ⁰ ^(t) −e ^(−(2πf) ⁰ ⁾ ² ^(/2))e−t ² ^(/2)  (13)where f₀ is the central frequency of the mother wavelet. The second termin the parenthesis is known as the correction term, as it corrects forthe non-zero mean of the complex sinusoid within the Gaussian window. Inpractice, it becomes negligible for values of f₀>>0 and can be ignored,in which case, the Morlet wavelet can be written in a simpler form as

$\begin{matrix}{{\psi(t)} = {\frac{1}{\pi^{1/4}}{\mathbb{e}}^{{\mathbb{i}2\pi}\; f_{0}t}{\mathbb{e}}^{{- t^{2}}/2}}} & (14)\end{matrix}$

This wavelet is a complex wave within a scaled Gaussian envelope. Whileboth definitions of the Morlet wavelet are included herein, the functionof equation (14) is not strictly a wavelet as it has a non-zero mean(i.e., the zero frequency term of its corresponding energy spectrum isnon-zero). However, it will be recognized by those skilled in the artthat equation (14) may be used in practice with f₀>>0 with minimal errorand is included (as well as other similar near wavelet functions) in thedefinition of a wavelet herein. A more detailed overview of theunderlying wavelet theory, including the definition of a waveletfunction, can be found in the general literature. Discussed herein ishow wavelet transform features may be extracted from the waveletdecomposition of signals. For example, wavelet decomposition of PPGsignals may be used to provide clinically useful information within amedical device.

Pertinent repeating features in a signal give rise to a time-scale bandin wavelet space or a resealed wavelet space. For example, the pulsecomponent of a PPG signal produces a dominant band in wavelet space ator around the pulse frequency. FIGS. 3( a) and (b) show two views of anillustrative scalogram derived from a PPG signal, according to anembodiment. The figures show an example of the band caused by the pulsecomponent in such a signal. The pulse band is located between the dashedlines in the plot of FIG. 3( a). The band is formed from a series ofdominant coalescing features across the scalogram. This can be clearlyseen as a raised band across the transform surface in FIG. 3( b) locatedwithin the region of scales indicated by the arrow in the plot(corresponding to 60 beats per minute). The maxima of this band withrespect to scale is the ridge. The locus of the ridge is shown as ablack curve on top of the band in FIG. 3( b). By employing a suitableresealing of the scalogram, such as that given in equation (11), theridges found in wavelet space may be related to the instantaneousfrequency of the signal. In this way, the pulse rate may be obtainedfrom the PPG signal. Instead of resealing the scalogram, a suitablepredefined relationship between the scale obtained from the ridge on thewavelet surface and the actual pulse rate may also be used to determinethe pulse rate.

By mapping the time-scale coordinates of the pulse ridge onto thewavelet phase information gained through the wavelet transform,individual pulses may be captured. In this way, both times betweenindividual pulses and the timing of components within each pulse may bemonitored and used to detect heart beat anomalies, measure arterialsystem compliance, or perform any other suitable calculations ordiagnostics. Alternative definitions of a ridge may be employed.Alternative relationships between the ridge and the pulse frequency ofoccurrence may be employed.

As discussed above, pertinent repeating features in the signal give riseto a time-scale band in wavelet space or a resealed wavelet space. For aperiodic signal, this band remains at a constant scale in the time-scaleplane. For many real signals, especially biological signals, the bandmay be non-stationary; varying in scale, amplitude, or both over time.FIG. 3( c) shows an illustrative schematic of a wavelet transform of asignal containing two pertinent components leading to two bands in thetransform space, according to an embodiment. These bands are labeledband A and band B on the three-dimensional schematic of the waveletsurface. In this embodiment, the band ridge is defined as the locus ofthe peak values of these bands with respect to scale. For purposes ofdiscussion, it may be assumed that band B contains the signalinformation of interest. This will be referred to as the “primary band”.In addition, it may be assumed that the system from which the signaloriginates, and from which the transform is subsequently derived,exhibits some form of coupling between the signal components in band Aand band B. When noise or other erroneous features are present in thesignal with similar spectral characteristics of the features of band Bthen the information within band B can become ambiguous (i.e., obscured,fragmented or missing). In this case, the ridge of band A may befollowed in wavelet space and extracted either as an amplitude signal ora scale signal which will be referred to as the “ridge amplitudeperturbation” (RAP) signal and the “ridge scale perturbation” (RSP)signal, respectively. The RAP and RSP signals may be extracted byprojecting the ridge onto the time-amplitude or time-scale planes,respectively. The top plots of FIG. 3( d) show a schematic of the RAPand RSP signals associated with ridge A in FIG. 3( c). Below these RAPand RSP signals are schematics of a further wavelet decomposition ofthese newly derived signals. This secondary wavelet decomposition allowsfor information in the region of band B in FIG. 3( c) to be madeavailable as band C and band D. The ridges of bands C and D may serve asinstantaneous time-scale characteristic measures of the signalcomponents causing bands C and D. This technique, which will be referredto herein as secondary wavelet feature decoupling (SWFD), may allowinformation concerning the nature of the signal components associatedwith the underlying physical process causing the primary band B (FIG. 3(c)) to be extracted when band B itself is obscured in the presence ofnoise or other erroneous signal features.

In some instances, an inverse continuous wavelet transform may bedesired, such as when modifications to a scalogram (or modifications tothe coefficients of a transformed signal) have been made in order to,for example, remove artifacts. In one embodiment, there is an inversecontinuous wavelet transform which allows the original signal to berecovered from its wavelet transform by integrating over all scales andlocations, a and b:

$\begin{matrix}{{x(t)} = {\frac{1}{C_{g}}{\int_{- \infty}^{\infty}{\int_{0}^{\infty}{{T\left( {a,b} \right)}\frac{1}{\sqrt{a}}{\psi\left( \frac{t - b}{a} \right)}\frac{{\mathbb{d}a}{\mathbb{d}b}}{a^{2}}}}}}} & (15)\end{matrix}$which may also be written as:

$\begin{matrix}{{x(t)} = {\frac{1}{C_{g}}{\int_{- \infty}^{\infty}{\int_{0}^{\infty}{{T\left( {a,b} \right)}{\psi_{a,b}(t)}\frac{{\mathbb{d}a}{\mathbb{d}b}}{a^{2}}}}}}} & (16)\end{matrix}$where C_(g) is a scalar value known as the admissibility constant. It iswavelet type dependent and may be calculated from:

$\begin{matrix}{C_{g} = {\int_{0}^{\infty}{\frac{{{\hat{\psi}(f)}}^{2}}{f}\ {\mathbb{d}f}}}} & (17)\end{matrix}$FIG. 3( e) is a flow chart of illustrative steps that may be taken toperform an inverse continuous wavelet transform in accordance with theabove discussion. An approximation to the inverse transform may be madeby considering equation (15) to be a series of convolutions acrossscales. It shall be understood that there is no complex conjugate here,unlike for the cross correlations of the forward transform. As well asintegrating over all of a and b for each time t, this equation may alsotake advantage of the convolution theorem which allows the inversewavelet transform to be executed using a series of multiplications. FIG.3( f) is a flow chart of illustrative steps that may be taken to performan approximation of an inverse continuous wavelet transform. It will beunderstood that any other suitable technique for performing an inversecontinuous wavelet transform may be used in accordance with the presentdisclosure.

FIG. 4 is an illustrative continuous wavelet processing system inaccordance with an embodiment. In this embodiment, input signalgenerator 410 generates an input signal 416. As illustrated, inputsignal generator 410 may include oximeter 420 coupled to sensor 418,which may provide as input signal 416, a PPG signal. It will beunderstood that input signal generator 410 may include any suitablesignal source, signal generating data, signal generating equipment, orany combination thereof to produce signal 416. Signal 416 may be anysuitable signal or signals, such as, for example, biosignals (e.g.,electrocardiogram, electroencephalogram, electrogastrogram,electromyogram, heart rate signals, pathological sounds, ultrasound, orany other suitable biosignal), dynamic signals, non-destructive testingsignals, condition monitoring signals, fluid signals, geophysicalsignals, astronomical signals, electrical signals, financial signalsincluding financial indices, sound and speech signals, chemical signals,meteorological signals including climate signals, and/or any othersuitable signal, and/or any combination thereof.

In this embodiment, signal 416 may be coupled to processor 412.Processor 412 may be any suitable software, firmware, and/or hardware,and/or combinations thereof for processing signal 416. For example,processor 412 may include one or more hardware processors (e.g.,integrated circuits), one or more software modules, computer-readablemedia such as memory, firmware, or any combination thereof. Processor412 may, for example, be a computer or may be one or more chips (i.e.,integrated circuits). Processor 412 may perform the calculationsassociated with the continuous wavelet transforms of the presentdisclosure as well as the calculations associated with any suitableinterrogations of the transforms. Processor 412 may perform any suitablesignal processing of signal 416 to filter signal 416, such as anysuitable band-pass filtering, adaptive filtering, closed-loop filtering,and/or any other suitable filtering, and/or any combination thereof.

Processor 412 may be coupled to one or more memory devices (not shown)or incorporate one or more memory devices such as any suitable volatilememory device (e.g., RAM, registers, etc.), non-volatile memory device(e.g., ROM, EPROM, magnetic storage device, optical storage device,flash memory, etc.), or both. The memory may be used by processor 412to, for example, store data corresponding to a continuous wavelettransform of input signal 416, such as data representing a scalogram. Inone embodiment, data representing a scalogram may be stored in RAM ormemory internal to processor 412 as any suitable three-dimensional datastructure such as a three-dimensional array that represents thescalogram as energy levels in a time-scale plane. Any other suitabledata structure may be used to store data representing a scalogram.

Processor 412 may be coupled to output 414. Output 414 may be anysuitable output device such as, for example, one or more medical devices(e.g., a medical monitor that displays various physiological parameters,a medical alarm, or any other suitable medical device that eitherdisplays physiological parameters or uses the output of processor 412 asan input), one or more display devices (e.g., monitor, PDA, mobilephone, any other suitable display device, or any combination thereof),one or more audio devices, one or more memory devices (e.g., hard diskdrive, flash memory, RAM, optical disk, any other suitable memorydevice, or any combination thereof), one or more printing devices, anyother suitable output device, or any combination thereof.

It will be understood that system 400 may be incorporated into system 10(FIGS. 1 and 2) in which, for example, input signal generator 410 may beimplemented as parts of sensor 12 and monitor 14 and processor 412 maybe implemented as part of monitor 14.

FIG. 5 shows a plot of an illustrative scalogram 500. For example,scalogram 500 may be generated from a PPG signal using the same method(e.g., using a continuous wavelet transform) that was used to derive thescalograms shown in FIGS. 3( a), 3(b), and 3(c). The scalogram of thetransform of any suitable signal may be generated or otherwise obtainedusing, for example a processor such as processor 412 (FIG. 4) ormicroprocessor 48 (FIG. 2).

Scalogram 500 includes edge effect regions 510 (also referred to hereinas wedge regions). As described above, a wavelet transform (e.g., acontinuous wavelet transform) of a signal may be performed by computinga convolution (or any other suitable cross-correlation) of the signalwith wavelets at various scales. Irrespective of the particular methodused to compute the transform, due to the finite extent of the signal,edge effects will be present. Within the edge effect region of thescalogram any computed transform values may be incomplete because thesignal values required to fully resolve the transform for a particulartime period may not be known or available. For example, the unknownsignal values may correspond to portions of the signal before knownsignal values (i.e., signal values preceding the start of signalmonitoring) or to portion of the signal after known signal values (i.e.,signal values that have not yet arrived). The edge effect region may belonger at larger scales because it takes longer (i.e., requires a largersignal portion) to fully resolve the wavelet transform of a signal atlarger scales.

Scalogram 500 illustrates the transform of a signal portion that spansfrom time t₀ to t₃. Edge effect regions 510 of scalogram 500 may containerroneous energy values resulting from apparent sharp discontinuities ateither end of the signal portion. This is because the wavelet transformcan only be computed using the known signal portion values.Computationally the effect of the signal ends on the transform may beequivalent to setting the unavailable signal values to zero. This largediscontinuity at the signal ends may result in the sharp discontinuitiesin scalogram 500 that defines edge effect regions 510.

At higher scales (e.g., the top portion of scalogram 500) the smallerwavelet scale sizes may result in a smaller edge effect region. At lowerscales (e.g., the bottom portion of scalogram 500) the larger waveletscale sizes may result in a larger edge effect region. Similarly,degrees of resolution to which the wavelet transform of the signal iscomputed may also effect the size of the edge effect region. A lowerresolution may result in a smaller edge effect region, while a higherresolution may result in a larger edge effect region. For discretewavelets, having a finite extent, the whole wavelet may be used. Forcontinuous wavelets (e.g., the Mortlet wavelet), which have atheoretically infinite extent, the degree of resolution may define thepoint at which the error between the true wavelet transform and thecomputed wavelet transform is acceptable for the purposes of thecomputation. In an embodiment, the Morlet wavelet may be cut-offapproximately three standard deviations from the center of the Gaussianwindow forming part of the wavelet function. The degree of resolutionmay be determined or adjusted by a user or patient using, e.g., usinguser inputs 56 (FIG. 2).

While the edge effect regions discussed herein are generally describedas occurring at the end of a signal, it should be understood that theedge effect region may refer to any region of the scalogram in whichthere are erroneous values resulting from large discontinuities in thesignal. For example, an edge effect region may also occur when there isa temporary loss of signal or where there is a large amount of noiseand/or artifacts that disrupt the signal.

FIG. 6 shows a plot of an illustrative signal 610 and an illustrativescalogram 620 generated from signal 610 and that schematicallyillustrates a process for estimating values for a transform using asignal estimate. Scalogram 620 may be derived from signal 610 using thesame method (e.g., using a continuous wavelet transform) that was usedto derive the scalograms shown in FIGS. 3( a), 3(b), 3(c), and 5. Signalportion 612 is a portion of a known signal that ends at time t₁. Signalportion 612 may be, for example, a PPG signals obtained from a patient,such as patient 40 (FIG. 2), using a sensor such as sensor 12 (FIG. 1).Scalogram portion 622 is a portion of scalogram 620 that was generatedfrom signal portion 612. Scalogram portion 622 includes edge effectregion 624 which was generated as a result of the end of signal portion612 at time t₁.

As illustrated in FIG. 6, estimated transform values for edge effectregion 624 of scalogram 620 may be generated using values estimated forthe, as yet unknown, portion of signal 610 after time t₁ (i.e. signalportion 616). Generating estimated transform values using an estimatedsignal portion may limit the effect of the discontinuity at the end ofsignal portion 612 on edge effect region 624 of scalogram 620. Theestimated values of signal portion 616 may then be replaced and/orupdated as new values for signal 610 are obtained. Similarly, theestimated transform values of edge effect region 624 of scalogram 620may also be replaced and/or updated based on the new values obtained forsignal 610.

The estimated values for signal 610 may be represented by estimatedsignal portion 616. Estimated signal portion 616 may be determined basedon the values of signal portion 612. For example, estimated signalportion 616 may be estimated as a constant value, as an extrapolation ofprevious signal values, or as a known signal type having determinedcharacteristic values. An illustrative process for determining valuesfor an estimated signal portion is described below with respect to FIG.8. The transform of signal 610 may be computed using the values ofestimated signal portion 616 and this transform may be used to generatescalogram 620 including estimated edge effect region 624. Estimated edgeeffect region 624 may be generated from the values of estimated signalportion 616. As illustrated, the length of estimated signal portion 616(i.e., the period of time between t₁ and t₂) may be approximately equalto the maximum length of estimated edge effect region 624 (i.e., theperiod of time between t₀ and t₁). In this example, the entire edgeeffect region 624 (i.e., the period of time between t₀ and t₁) isestimated up to and including the largest wavelet scale sizes (i.e., atthe lowest scales) illustrated in scalogram 600. If estimated transformvalues are only needed for higher scales (i.e., smaller scale sizes), ashorter estimated signal portion may be used to generate an estimatedscalogram portion that provides estimated transform values for thenecessary scales. As described above with respect to the scalogramsshown in FIGS. 3( a), 3(b), and 3(c), scalogram 600 including estimatededge effect region 624 may be processed to determine one or moreparameters or characteristics of signal 610. Replacing the erroneousvalues of edge effect region 624 with estimated values may simplifyand/or improve the processing of scalogram 600 to determine theseparameters. For example, a PPG signal transformed in this manner may beused to determine a blood oxygen saturation value, a respiration rate, arespiration effort metric, or another suitable biological parameter. Inan embodiment, in addition to estimating edge effect region 624 based onestimated signal portion 616, scalogram portion 626 may also beestimated based on estimated signal portion 616. Furthermore, estimatedsignal portion 616 may be extended beyond time t₂ to estimate scalogramportion 626 or additional scalogram portions.

FIG. 7 depicts an illustrative process 700 for determining parameters ofa signal using estimated transform values generated from signalestimates. Process 700 may be implemented in a pulse oximetry systemsuch as pulse oximetry system 10 (FIG. 1), and the steps of process 700may be carried out using a processor such as processor 412 (FIG. 4) ormicroprocessor 48 (FIG. 2).

Process 700 may start at step 710. At step 720, a first portion of asignal may be obtained. The first portion of the signal may be a portionof a PPG signal or any other suitable biosignal or general signal. Forexample, the signal portion may be obtained from pulse oximetry system10 (FIG. 1) using a sensor such as sensor 12 (FIG. 1) to measurebiological parameters of a patient such as patient 40 (FIG. 2).Alternatively, the signal may be obtained by averaging or otherwisecombining multiple signals derived from a suitable sensor array, asdiscussed in relation to FIG. 1. Further, the signal may be obtainedfrom a source other than pulse oximeter system 10 (FIG. 1). For example,a signal may be obtained from another type of medical device or fromnon-medical devices including a general signal oscilloscope and/orwaveform analyzer.

The signal obtained in step 720 may be obtained by processing apreliminary signal. For example, a preliminary PPG signal may beobtained using, e.g., sensor 12 (FIG. 1) and processed using a processorsuch as processor 412 (FIG. 4) or microprocessor 48 (FIG. 2) in a systemsimilar or identical to pulse oximetry system 10 (FIG. 1). The signalobtained at step 720 may have been processed by methods including, forexample, normalization, low-pass filtering, removal of noise-components,and/or interpolation methods to remove various undesirable artifactsthat may be present in the preliminary signal.

At step 730 a second portion of the signal may be estimated. The portionof the signal obtained in step 720 may be a portion of a real-timesignal or it may be a portion of a signal previously obtained and storedin memory, for example, ROM 52 (FIG. 2) or RAM 54 (FIG. 2) and that canbe accessed and/or processed in real-time. Values for a portion of thesignal that are not be currently known may be estimated. The estimatedsignal portion may include signal values that have not yet been receivedand/or processed. For example, the portion of the signal obtained instep 720 may represent a current portion of a real-time signal and theportion of the signal estimated in step 730 may represent future valuesof the signal. As another example, the portion of the signal obtained instep 720 may represent a generated signal and the portion of the signalestimated in step 730 may represent values of the signal that have notyet been generated. The estimated signal portion is not limited tosignal values that follow the obtained signal portion, the unavailableportion may also include, for example, values of prior portions thatwere never obtained or that are no longer available.

Furthermore, the second signal portion estimated in step 730 may be asignal portion associated with obtained values that are obscured bysignal noise and/or artifacts (including, for example, portion of thesignal obtained in step 720). For example) a PPG signal may containerroneous or otherwise undesirable artifacts due to, for example,patient movement, equipment failure, and/or various noise sources. Forexample, cable 24, cable 32, and/or cable 34 (all of FIG. 1) maymalfunction or become loosened from the equipment to which it isconnected. Further, sensor 12 (FIG. 1), or any constituent component ofsensor 12 (FIG. 1) (for example, emitter 16 (FIG. 1) and/or detector 18(FIG. 1)) may malfunction and/or become loosened. Additionally, noisesources may produce inconsistent features in a PPG signal or otherbiosignal. Possible sources of noise include thermal noise, shot noise,flicker noise, burst noise, and/or electrical noise caused by lightpollution. These and other noise sources may be introduced, for example,through sensor 12 (FIG. 1), and/or cables 24, 32, and 34 (all of FIG.1). These and/or other phenomena may be present in a system such aspulse oximetry system 10 (FIG. 1), and thus may introduce inconsistentfeatures into a PPG signal.

At step 730 values for the second portion of the signal, correspondingto an unknown or erroneous portion of the signal, may be estimated basedon the values of the portion of the signal obtained in step 720. Thesecond portion of the signal may be estimated as a constant value, as anextrapolation of previous signal values, or may be estimated using anyother suitable approach. Alternatively and/or additionally, where thesecond portion of the signal corresponds to obtained signal values thatare obscured by noise or artifacts, the second portion of the signal maybe estimated by filtering, interpolating or smoothing the obtainedvalues of this signal portion to minimize the effects of theseundesirable signal elements. These and other estimation techniques maybe implemented in pulse oximetry system 10 (FIG. 1) by processor 412(FIG. 4), microprocessor 48 (FIG. 2), ROM 52 (FIG. 2), and/or RAM 54(FIG. 2). A plot the signal portions may be displayed using any suitabledisplay device such as, for example, monitor 20 (FIG. 1), display 28(FIG. 1), a PDA, a mobile device, any other suitable display device, ormultiple display devices. An illustrative process for estimating aportion of the signal in step 730 is described in greater detail belowwith respect to FIG. 8.

At step 740 the signal portions obtained in steps 720 and 730 may betransformed (e.g., using a continuous wavelet transform). As describedabove with respect to FIG. 5 and FIG. 6, using the values of the signalportion estimated in step 730 to compute the transform of the signalportion obtained in step 720 may reduce the erroneous energy levelsgenerated within the transform. The erroneous energy portions within theedge effect regions (or any other regions of the transform affected byunknown or erroneous signal data) may be replaced by estimated transformvalues. The transformation of the signal portions may be performedusing, for example a processor such as processor 412 (FIG. 4) ormicroprocessor 48 (FIG. 2). An illustrative process for transforming thesignal at step 740 is described below with respect to FIG. 9.

At step 750 one or more parameters of the signal may be determined fromthe transformed signal including the estimated transform values. Forexample, a PPG signal transformed in this manner may be used todetermine a blood oxygen saturation value, a respiration rate, arespiration effort metric, or another suitable biological parameter. Inan embodiment, a scalogram may be generated from the transformed signalusing the same approach that was used to derive the scalograms shown inFIGS. 3( a), 3(b), 3(c), 5, and 6. The scalogram of the transformedsignal may be generated or otherwise obtained using, for example aprocessor such as processor 412 (FIG. 4) or microprocessor 48 (FIG. 2).In addition to the scalogram, other parts of the wavelet transform maybe determined. For example, the transform modulus, phase, real, and/orimaginary parts may be generated in addition to the scalogram. Thegenerated scalograms may be displayed, for example, on monitor 26(FIG. 1) or display 20 or 28 (both of FIG. 1).

The resultant scalogram may include bands and ridges corresponding to atleast one area of increased energy. For example, a respiration band ofthe scalogram may generally reflect the breathing pattern of a patient,e.g., patient 40 (FIG. 2). These bands may be extracted from thescalogram using, for example, a processor such as processor 412 (FIG. 4)or microprocessor 48 (FIG. 2), using any suitable method. Therespiration band of the scalogram may be identified usingcharacteristics of the scalogram including the energy and structure ofthe scalogram, and the signal-to-noise levels in various regions ofscalogram. One or more of the parameters may be determined at step 750from the identified characteristics of the scalogram.

Finally, at step 760 the signal parameters determined in step 750 may bereported. For example, the parameters may be reported by generating anaudible alert or, for example, using speaker 22 (FIG. 2) as well aspossibly through other audio devices, generating an on-screen message,for example, on display 20 (FIG. 1) or display 28 (FIG. 1), generating apager message, a text message, or a telephone call, for example, using awireless connection embedded or attached to a system such as system 10(FIG. 1), activating a secondary or backup sensor or sensor array, forexample, connected through a wire or wirelessly to monitor 14 (FIG. 1),or regulating the automatic administration of medicine, for example,which is controlled in part or fully through a system such as system 10(FIG. 1). Additionally, the signal parameters may be reported on adisplay such as display 20 (FIG. 1) or display 28 (FIG. 1) in graphicalform using, for example, a bar graph or histogram. The signal parametersmay also be reported to one or more other processes, for example, to beused as part of or to improve the reliability of other measurements orcalculations within a system such as pulse oximetry system 10 (FIG. 1).

FIG. 8 depicts an illustrative process 800 for estimating the values ofa portion of a signal. Process 800 may be implemented in a pulseoximetry system such as pulse oximetry system 10 (FIG. 1) to estimate aportion of a PPG signal, and the steps of process 800 may be carried outusing a processor such as processor 412 (FIG. 4) or microprocessor 48(FIG. 2). Process 800 may correspond to a further embodiment of aportion of process 700 (FIG. 7), and more particularly, may correspondto a further embodiment of step 730.

Process 800 may start at step 810. At step 810, a portion of a signalmay be selected for estimation. The selected signal portion may be anunknown portion of the signal such as a portion of the signal that isnot available or that has not yet arrived (i.e., a future or past signalportion). The selected signal portion may also be a portion of thesignal that is obscured by noise and/or artifacts. In an embodiment, thesignal portion may be selected based on a scalogram generated from thesignal. For example, the selected portion of the signal may correspondto a region of the scalogram that has erroneous values such as an edgeeffect region. After the region of the scalogram is identified, a signalportion corresponding to that region may be selected for estimation.

The signal portion selected for estimation at step 810 may be selectedautomatically. For example, a portion of the signal that follows theleading edge of the signal may be selected automatically for estimation.As another example, a noisy or otherwise obscured portion of the signalmay be selected automatically for estimation. These and other techniquesmay be implemented in pulse oximetry system 10 (FIG. 1) by processor 412(FIG. 4), microprocessor 48 (FIG. 2), ROM 52 (FIG. 2), and/or RAM 54(FIG. 2). Additionally, the parameters that may be used to select asignal portion for estimation may be controlled by a user or patient,e.g., using user inputs 56 (FIG. 2). The signal portion selected forestimation may be displayed, for example, on monitor 26 (FIG. 1) ordisplay 20 or 28 (both of FIG. 1). Alternatively, a signal may bedisplayed on a monitor, and a user may choose or otherwise influencewhich portion of the signal (including unknown portions of the signal)is selected using, for example, user inputs 56 (FIG. 2). While process800 is described primarily with respect to a single estimated signalportion, it should be understood that multiple signal portions may alsobe selected for estimation in accordance with this process.

At step 820 the known portions of the signal may be analyzed todetermine whether the signal is a known signal type. The type of signalmay be determined based on the type of system and/or sensor used toobtain the signal. For example, the signal received by pulse oximetrysystem 10 (FIG. 1) may be determined to be a PPG signal. The signal typemay also be determined based on the characteristics of the signal. Forexample, the signal may be determined to be a PPG signal based on thesize, shape, or frequency of the signal. These and other techniques maybe implemented in pulse oximetry system 10 (FIG. 1) by processor 412(FIG. 4), microprocessor 48 (FIG. 2), ROM 52 (FIG. 2), and/or RAM 54(FIG. 2). For example, the signal analyzed in step 820 may be comparedwith a library of known signal types that may be stored in ROM 52 (FIG.2), and/or RAM 54 (FIG. 2) by processor 412 (FIG. 4) and/ormicroprocessor 48 (FIG. 2). Additionally, the signal type may beselected by a user or patient using, e.g., using user inputs 56 (FIG.2).

If it is determined at step 820 that the signal is a known signal type,at step 830 values of the signal portion selected in step 810 may beestimated. The values of the signal portion selected in step 810 may beestimated at step 830 by determining characteristic values of the knownsignal portions and estimating signal values based on the characteristicvalues of the known signal type. For example, if the signal is a PPGsignal, values of the signal portion selected in step 810 may beestimated based on the characteristic values of the signal such as thesize, shape and/or rate of the pulses in the PPG signal. If one or moreof the determined characteristic values of the signal are determined tobe stable, those values may be used to estimate the values of theselected signal portion of the PPG signal. For example, if the pulsesize and shape of a PPG signal are determined to be stable but the pulserate is not stable, only the characteristic values of the pulse size andshape may be used to estimate the values of the selected signal portion.According to this example, if the known portion of a PPG signal ends inthe middle of a pulse, the values for the following portion of thesignal may be estimated using the characteristic values of the shape andsize of the pulse. Additionally and/or alternatively known signal typesmay be estimated based on information about the origin of the signal.For example, if the signal is a PPG signal information about typicalpulse sizes and pulse rates may be used to help estimate the signal.Further, information obtained from other biosignals having knownrelationships to a PPG signal may also be used to estimate the signal.If values for the selected signal portion cannot be estimated using thistechnique, the signal values may be estimated using the techniquesdescribed below with respect to steps 850 and 860 or by using any othersuitable estimation techniques.

If it is determined at step 820 that the signal is not a known signaltype, at step 840 it is determined whether the signal fits a curve orany other type of function. If it is determined at step 840 that thesignal fits a curve, signal values may be estimated at step 850 using anextrapolated estimate or fitted curve (i.e., a functional estimate) toestimate the signal. This determination may use, for example,self-optimizing/predictive neural networks, the projection of ensembleaveraged historic data, non-linear extrapolation of historic data (e.g.,through cubic spline fitting or other multi-order estimates), or anyother suitable techniques. If these techniques are not sufficient toestimate the values for the selected signal portion, the values of theselected signal portion may be estimated using the techniques describedbelow with respect to step 860 or any other suitable estimationtechnique.

If it is determined at step 840 that the signal cannot be fit to a curveor other function, at step 860 values of the signal portion selected instep 810 may be estimated as a constant value. The estimated constantvalue may be, for example, a known signal value closest in time to thesignal portion selected for estimation in step 810, a mean or medianvalue of the know portions of the signal, or any other suitable value.In an alternative embodiment, the signal may be estimated to approach aconstant value (e.g., its mean value) smoothly over time. This may beadvantageous in avoiding sudden transient features and discontinuitiesin the estimated signal. These and other signal estimation techniquesmay be implemented in pulse oximetry system 10 (FIG. 1) by processor 412(FIG. 4), microprocessor 48 (FIG. 2), ROM 52 (FIG. 2), and/or RAM 54(FIG. 2). Additionally, the techniques used to estimate the signalportion and/or the parameters of the estimation may be controlled by auser or patient, e.g., using user inputs 56 (FIG. 2).

In addition to estimating values for a selected signal portion, aconfidence value may also be determined in accordance with process 800.The confidence value may represent a relative confidence in an accuracyof the determination. The confidence value may be represented by anumber from 1 to 100, where a larger number indicates a high confidencevalue in the estimation (any other suitable number range could be usedinstead). The confidence value may be determined based on the length ofthe signal portion to be estimated, the length of the known signalportions used to estimate the signal values, the technique used toestimate the signal values, a determination of the accuracy of theestimation, etc. The confidence value may also be determined based onthe determined accuracy of estimated transform values obtained from theestimated signal portion (e.g., at step 740 of FIG. 7) and/or based onactual values of the estimated signal portion when they becomeavailable.

At step 870 new signal values may be received. The received signalvalues may correspond to some of the values signal estimated in steps830, 850, and 860. The estimated signal values may be replaced with thereceived values. At step 880 the estimated signal values that were notreplaced with received signal values in step 870 may be updated with newestimates based on the received values. In addition to using thereceived signal values to update the estimated values, the estimationtechnique may be modified based on a comparison of the previouslyestimated values and the received values. If desired, process 800 mayreturn to step 810 to select new signal portions for estimation afterthe previously selected portion is updated with received signal values.The steps for determining an estimation technique (i.e., steps 820 and840) may be repeated or the same technique used for the previouslyselected portions may be used (as updated based on step 890, ifapplicable).

FIG. 9 depicts an illustrative process 900 for performing a transform ofa signal using estimated portions of the signal. Process 900 may beimplemented in a pulse oximetry system such as pulse oximetry system 10(FIG. 1) to perform a continuous wavelet transform on a PPG signalincluding estimated signal portions, and the steps of process 800 may becarried out using a processor such as processor 412 (FIG. 4) ormicroprocessor 48 (FIG. 2). Process 900 may correspond to a furtherembodiment of a portion of process 700 (FIG. 7), and more particularly,may correspond to a further embodiment of step 740.

Process 900 may start at step 910. At step 910 desired scales for thetransform may be determined. The desired scales may correspond to theentire range of scales within a scalogram (e.g. the range of scalesdisplayed within FIGS. 5 and 6). The desired scales may also correspondto a range of scales associated with a particular feature or parameterthat is being determined. For example, the desired bands of a PPGtransform may correspond to the scales associated with pulse orrespiration features. This determination of scales may be implemented inpulse oximetry system 10 (FIG. 1) by processor 412 (FIG. 4),microprocessor 48 (FIG. 2), ROM 52 (FIG. 2), and/or RAM 54 (FIG. 2). Ascalogram of the signal may be displayed, for example, on monitor 26(FIG. 1) or display 20 or 28 (both of FIG. 1) and a user or patient maychoose or otherwise influence which scales within the scalogram areselected using, for example, user inputs 56 (FIG. 2).

At step 920 portions of a signal are selected based on the scalesdetermined in step 910. The portions of the signal selected at step 920include signal portions associated with known signal values (e.g., aportion of a signal obtained in step 720 (FIG. 7)) and signal portionsassociated with estimated signal values. The selected signal portionsmay include signal portions associated with known signal values that maybe used to compute a transform of the signal at the desired scales. Theselected signal portions may also include signal portions associatedwith estimated signal values that may be used together with the knownsignal values to compute a transform of the signal at the desiredscales. As illustrated above with respect to FIGS. 5 and 6, at higherscales the smaller wavelet sizes may be used to compute a transform of asignal for a given time period using a relatively smaller portion of thesignal than would be required to compute a transform of the signal forthe same time period with the larger wavelet sizes at lower scales. Thisrelationship between scale and signal portion size may be illustrated bythe edge effect regions of FIGS. 5 and 6 in which signal edges (and thecorresponding lack of additional signal values beyond the edges) areshown to cause larger edge effect regions at the lower scales. Thereforefor a given time period the size of the selected estimated signalportions may depend on the desired scales selected in step 910. Thevalues for the selected estimated signal portions may be determined) forexample, in accordance with process 800 (FIG. 8). This selection ofsignal portions may be implemented in pulse oximetry system 10 (FIG. 1)by processor 412 (FIG. 4), microprocessor 48 (FIG. 2), ROM 52 (FIG. 2),and/or RAM 54 (FIG. 2). A plot of the signal and/or a scalogram of thesignal may be displayed, for example) on monitor 26 (FIG. 1) or display20 or 28 (both of FIG. 1) and a user or patient may choose or otherwiseinfluence which portions of the signal are selected using, for example,user inputs 56 (FIG. 2).

At step 930 a transform of the signal portions selected in step 920 maybe performed. For example, the selected signal portions may betransformed using a continuous wavelet transforms. As described above,using the estimated signal portions to compute the transform may reducethe erroneous energy generated within the transform. The erroneousenergy portions within the edge effect regions (or any other regions ofthe transform effected by unavailable or poor signal data) may bereplaced by estimated transform values. The transformation of the signalportions may be performed using, for example a processor such asprocessor 412 (FIG. 4) or microprocessor 48 (FIG. 2). A scalogram may begenerated from the transformed signal portions using the same approachthat was used to derive the scalograms shown in FIGS. 3( a), 3(b), 3(c),5, and 6. The scalogram of the transformed signal may be generated orotherwise obtained using, for example a processor such as processor 412(FIG. 4) or microprocessor 48 (FIG. 2).

At step 940 process 900 may wait to obtain new values for the signal. Ifnew signal values are obtained, the selected portions of the signal maybe updated at step 950. The new values may be used to replace previouslyestimated signal values. The new values may also be used to update orimprove the estimated values for portions of the signal whose values arestill unknown. The new values may also be used to estimate additionalsignal portions. For example, a sliding window (e.g., corresponding toan edge effect region of a range of scales) may be used to estimatesignal portions for a particular time period following the last knownsignal value. As new values of the signal are obtained this window mayadvance to a next portion of the signal. Process 900 may then continueto transform of the updated signal portions at step 930. In anembodiment, a transform of the entire updated signal portions may becalculated. In an embodiment, only a transform of the updated values maybe calculated and the previously calculated transform values may beupdated with the newly calculated transform values. These and othertechniques may be implemented in pulse oximetry system 10 (FIG. 1) byprocessor 412 (FIG. 4), microprocessor 48 (FIG. 2), ROM 52 (FIG. 2),and/or RAM 54 (FIG. 2).

It will also be understood that the above method may be implementedusing any human-readable or machine-readable instructions on anysuitable system or apparatus, such as those described herein.

1. A method for estimating transform values using a signal estimatecomprising: obtaining a first portion of a biological signal from asensor; estimating a second portion of the signal based at least in parton the first portion of the signal; performing a transform of the signalbased at least in part on the first portion of the signal and the secondportion of the signal; and determining a biological parametercorresponding to the signal based at least in part on the transformedsignal.
 2. The method of claim 1 wherein the biological signal comprisesa photoplethysmograph (PPG) signal and wherein the determined parametercomprises blood oxygen saturation level, respiration rate, respirationeffort metric, pulse rate, and/or blood pressure.
 3. The method of claim1 wherein the transform comprises a continuous wavelet transform.
 4. Themethod of claim 3 wherein estimating the second portion of the signalfurther comprises: selecting a range of scales for the continuouswavelet transform; and determining a length for the second portion ofthe signal based at least in part on the selected range of scales. 5.The method of claim 4 wherein selecting the range of scales for thecontinuous wavelet transform comprises locating one or more featureswithin a continuous wavelet transform of the signal.
 6. The method ofclaim 1 wherein estimating the second portion of the signal comprises:determining an amplitude value of the first portion of the signal;estimating the determined amplitude value as a constant value for thesecond signal.
 7. The method of claim 1 wherein estimating the secondportion of the signal comprises: fitting a function to the first portionof the signal; and estimating the second signal using the function. 8.The method of claim 1 wherein estimating the second portion of thesignal comprises: determining that the first portion of the signal is aknown signal type; determining one or more characteristic values of thefirst portion PPG signal; and estimating the second signal by generatinga signal portion of the known signal type having at least one of thedetermined characteristic values.
 9. The method of claim 1 furthercomprising determining an estimation confidence value for the secondportion of the signal.
 10. The method of claim 1 further comprisingupdating the transform of the signal in response to obtaining signalvalues corresponding to the second portion of the signal.
 11. The methodof claim 1 wherein the second signal portion is generally adjacent to anend of the first signal portion.
 12. The method of claim 1 wherein thesecond signal portion is generally within the first signal portion. 13.A system for processing a signal to estimate transform values using asignal estimate, the system comprising: a sensor to receive dataindicative of a biological signal; a processor coupled to the sensor,wherein the processor is capable of: obtaining a first portion of thereceived signal; estimating a second portion of the signal based atleast in part on the first portion of the signal; performing a wavelettransform of the signal based at least in part on the first portion ofthe signal and the second portion of the signal; and determining abiological parameter generally corresponding to the signal based atleast in past on the transformed signal.
 14. The system of claim 13wherein the biological signal comprises a photoplethysmograph (PPG)signal and wherein the determined parameter comprises blood oxygensaturation level, respiration rate, respiration effort metric, pulserate, and/or blood pressure.
 15. The system of claim 13 wherein theprocessor is further capable of: selecting a range of scales for thecontinuous wavelet transform; and determining a length for the secondportion of the signal based at least in pail on the selected range ofscales.
 16. The system of claim 15 wherein selecting the range of scalesfor the continuous wavelet transform comprises locating one or morefeatures within a continuous wavelet transform of the signal.
 17. Thesystem of claim 13 wherein the processor is further capable of:determining an amplitude value of the first portion of the signal;estimating the determined amplitude value as a constant value for thesecond signal.
 18. The system of claim 13 wherein the processor isfurther capable of: generally fitting a function to the first portion ofthe signal; and estimating the second signal using the function.
 19. Thesystem of claim 13 wherein the processor is further capable of:determining that the first portion of the signal is a known signal type;determining one or more characteristic values of the first portion PPGsignal; and estimating the second signal by generating a signal portionof the known signal type having at least one of the determinedcharacteristic values.
 20. The system of claim 13 wherein the processoris further capable of determining an estimation confidence value for thesecond portion of the signal.